There's no real mechanism for securing the cover; it's pretty much just held down by its own weight plus whatever you put in it. TS included minimal information with the case, but one of the things they point out on their "owner's guide" is that the leather should break in over time and then, presumably, it'll stay closed more easily. They suggest setting the phone down with the camera facing up to help facilitate the break in process if the weight of any cards and cash in the wallet portion isn't enough to keep it closed.

In the case of a fall, I'd guess it'll be hit or miss whether the screen gets the protection of the cover, though it's worth noting that the composite portion of the case does extend slightly past the face of the phone so, regardless of whether the cover stays closed, it should serve decently for shock protection. As I was writing this I got curious and dropped it a few times from a couple feet up to see what would happen, and for what it's worth the cover actually seemed to naturally pull itself back to a closed position in the vast majority of my "tests."